Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 67.4% → 70.7%

Time: 1.9s

Alternatives: 7

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - x) * (z - t)) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Python

def code(x, y, z, t, a):
	return x + (((y - x) * (z - t)) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - x) * (z - t)) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - x) * (z - t)) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Python

def code(x, y, z, t, a):
	return x + (((y - x) * (z - t)) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - x) * (z - t)) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 70.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+219}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+168}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e+219)
   (- y x)
   (if (<= t 5.6e+168) (+ x (/ (* (- y x) (- z t)) (- a t))) (+ x (- y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+219) {
		tmp = y - x;
	} else if (t <= 5.6e+168) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = x + (y - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9d+219)) then
        tmp = y - x
    else if (t <= 5.6d+168) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else
        tmp = x + (y - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+219) {
		tmp = y - x;
	} else if (t <= 5.6e+168) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = x + (y - x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e+219:
		tmp = y - x
	elif t <= 5.6e+168:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	else:
		tmp = x + (y - x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e+219)
		tmp = Float64(y - x);
	elseif (t <= 5.6e+168)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e+219)
		tmp = y - x;
	elseif (t <= 5.6e+168)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	else
		tmp = x + (y - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e+219], N[(y - x), $MachinePrecision], If[LessEqual[t, 5.6e+168], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.00000000000000047e219

   1. Initial program 9.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

   5. Applied rewrites 3.8%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \color{blue}{\left(z - t\right)} \]

   8. Applied rewrites 48.8%

      \[\leadsto x + \left(y - \color{blue}{x}\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]

   11. Applied rewrites 49.5%

       \[\leadsto \color{blue}{y - x} \]

   if -9.00000000000000047e219 < t < 5.5999999999999998e168

   1. Initial program 76.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   if 5.5999999999999998e168 < t

   1. Initial program 30.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

   5. Applied rewrites 1.7%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \color{blue}{\left(z - t\right)} \]

   8. Applied rewrites 52.6%

      \[\leadsto x + \left(y - \color{blue}{x}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -3.45 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+188}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (- a t)))))
   (if (<= a -3.45e+133)
     t_1
     (if (<= a 2e+188) (/ (* (- y x) (- z t)) (- a t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a - t));
	double tmp;
	if (a <= -3.45e+133) {
		tmp = t_1;
	} else if (a <= 2e+188) {
		tmp = ((y - x) * (z - t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) / (a - t))
    if (a <= (-3.45d+133)) then
        tmp = t_1
    else if (a <= 2d+188) then
        tmp = ((y - x) * (z - t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a - t));
	double tmp;
	if (a <= -3.45e+133) {
		tmp = t_1;
	} else if (a <= 2e+188) {
		tmp = ((y - x) * (z - t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a - t))
	tmp = 0
	if a <= -3.45e+133:
		tmp = t_1
	elif a <= 2e+188:
		tmp = ((y - x) * (z - t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -3.45e+133)
		tmp = t_1;
	elseif (a <= 2e+188)
		tmp = Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -3.45e+133)
		tmp = t_1;
	elseif (a <= 2e+188)
		tmp = ((y - x) * (z - t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.45e+133], t$95$1, If[LessEqual[a, 2e+188], N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.4500000000000001e133 or 2e188 < a

   1. Initial program 66.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \frac{\color{blue}{y \cdot \left(z - t\right)}}{a - t} \]

   5. Applied rewrites 58.8%

      \[\leadsto x + \frac{\color{blue}{y - x}}{a - t} \]

   if -3.4500000000000001e133 < a < 2e188

   1. Initial program 64.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]

   5. Applied rewrites 51.8%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 32.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -8.4 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+24}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (- a t)))))
   (if (<= a -8.4e+114) t_1 (if (<= a 2.55e+24) (- y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a - t));
	double tmp;
	if (a <= -8.4e+114) {
		tmp = t_1;
	} else if (a <= 2.55e+24) {
		tmp = y - x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) / (a - t))
    if (a <= (-8.4d+114)) then
        tmp = t_1
    else if (a <= 2.55d+24) then
        tmp = y - x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a - t));
	double tmp;
	if (a <= -8.4e+114) {
		tmp = t_1;
	} else if (a <= 2.55e+24) {
		tmp = y - x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a - t))
	tmp = 0
	if a <= -8.4e+114:
		tmp = t_1
	elif a <= 2.55e+24:
		tmp = y - x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -8.4e+114)
		tmp = t_1;
	elseif (a <= 2.55e+24)
		tmp = Float64(y - x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -8.4e+114)
		tmp = t_1;
	elseif (a <= 2.55e+24)
		tmp = y - x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.4e+114], t$95$1, If[LessEqual[a, 2.55e+24], N[(y - x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.4000000000000001e114 or 2.5499999999999998e24 < a

   1. Initial program 68.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \frac{\color{blue}{y \cdot \left(z - t\right)}}{a - t} \]

   5. Applied rewrites 47.5%

      \[\leadsto x + \frac{\color{blue}{y - x}}{a - t} \]

   if -8.4000000000000001e114 < a < 2.5499999999999998e24

   1. Initial program 62.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

   5. Applied rewrites 13.9%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \color{blue}{\left(z - t\right)} \]

   8. Applied rewrites 27.6%

      \[\leadsto x + \left(y - \color{blue}{x}\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]

   11. Applied rewrites 28.0%

       \[\leadsto \color{blue}{y - x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 29.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+117}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-9}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.8e+117)
   (- y x)
   (if (<= t 2.35e-9) (+ x (* (- y x) (- z t))) (+ x (- y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e+117) {
		tmp = y - x;
	} else if (t <= 2.35e-9) {
		tmp = x + ((y - x) * (z - t));
	} else {
		tmp = x + (y - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.8d+117)) then
        tmp = y - x
    else if (t <= 2.35d-9) then
        tmp = x + ((y - x) * (z - t))
    else
        tmp = x + (y - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e+117) {
		tmp = y - x;
	} else if (t <= 2.35e-9) {
		tmp = x + ((y - x) * (z - t));
	} else {
		tmp = x + (y - x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.8e+117:
		tmp = y - x
	elif t <= 2.35e-9:
		tmp = x + ((y - x) * (z - t))
	else:
		tmp = x + (y - x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.8e+117)
		tmp = Float64(y - x);
	elseif (t <= 2.35e-9)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z - t)));
	else
		tmp = Float64(x + Float64(y - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.8e+117)
		tmp = y - x;
	elseif (t <= 2.35e-9)
		tmp = x + ((y - x) * (z - t));
	else
		tmp = x + (y - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.8e+117], N[(y - x), $MachinePrecision], If[LessEqual[t, 2.35e-9], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.79999999999999981e117

   1. Initial program 28.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

   5. Applied rewrites 3.5%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \color{blue}{\left(z - t\right)} \]

   8. Applied rewrites 35.0%

      \[\leadsto x + \left(y - \color{blue}{x}\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]

   11. Applied rewrites 35.3%

       \[\leadsto \color{blue}{y - x} \]

   if -7.79999999999999981e117 < t < 2.34999999999999995e-9

   1. Initial program 87.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

   5. Applied rewrites 26.4%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

   if 2.34999999999999995e-9 < t

   1. Initial program 42.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

   5. Applied rewrites 2.2%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \color{blue}{\left(z - t\right)} \]

   8. Applied rewrites 41.2%

      \[\leadsto x + \left(y - \color{blue}{x}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 23.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - t\right)\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+146}:\\ \;\;\;\;x + \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- a t))))
   (if (<= x -4.3e+99) t_1 (if (<= x 1.4e+146) (+ x (- y x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a - t);
	double tmp;
	if (x <= -4.3e+99) {
		tmp = t_1;
	} else if (x <= 1.4e+146) {
		tmp = x + (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a - t)
    if (x <= (-4.3d+99)) then
        tmp = t_1
    else if (x <= 1.4d+146) then
        tmp = x + (y - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a - t);
	double tmp;
	if (x <= -4.3e+99) {
		tmp = t_1;
	} else if (x <= 1.4e+146) {
		tmp = x + (y - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a - t)
	tmp = 0
	if x <= -4.3e+99:
		tmp = t_1
	elif x <= 1.4e+146:
		tmp = x + (y - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a - t))
	tmp = 0.0
	if (x <= -4.3e+99)
		tmp = t_1;
	elseif (x <= 1.4e+146)
		tmp = Float64(x + Float64(y - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a - t);
	tmp = 0.0;
	if (x <= -4.3e+99)
		tmp = t_1;
	elseif (x <= 1.4e+146)
		tmp = x + (y - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e+99], t$95$1, If[LessEqual[x, 1.4e+146], N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3000000000000001e99 or 1.4e146 < x

   1. Initial program 51.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

   5. Applied rewrites 25.1%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \color{blue}{\left(z - t\right)} \]

   8. Applied rewrites 5.2%

      \[\leadsto x + \left(y - \color{blue}{x}\right) \]

   9. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} \]

   11. Applied rewrites 24.4%

       \[\leadsto x + \color{blue}{\left(a - t\right)} \]

   if -4.3000000000000001e99 < x < 1.4e146

   1. Initial program 69.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

   5. Applied rewrites 12.4%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \color{blue}{\left(z - t\right)} \]

   8. Applied rewrites 26.3%

      \[\leadsto x + \left(y - \color{blue}{x}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 23.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - t\right)\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+147}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- a t))))
   (if (<= x -4.3e+99) t_1 (if (<= x 5.2e+147) (- y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a - t);
	double tmp;
	if (x <= -4.3e+99) {
		tmp = t_1;
	} else if (x <= 5.2e+147) {
		tmp = y - x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a - t)
    if (x <= (-4.3d+99)) then
        tmp = t_1
    else if (x <= 5.2d+147) then
        tmp = y - x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a - t);
	double tmp;
	if (x <= -4.3e+99) {
		tmp = t_1;
	} else if (x <= 5.2e+147) {
		tmp = y - x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a - t)
	tmp = 0
	if x <= -4.3e+99:
		tmp = t_1
	elif x <= 5.2e+147:
		tmp = y - x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a - t))
	tmp = 0.0
	if (x <= -4.3e+99)
		tmp = t_1;
	elseif (x <= 5.2e+147)
		tmp = Float64(y - x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a - t);
	tmp = 0.0;
	if (x <= -4.3e+99)
		tmp = t_1;
	elseif (x <= 5.2e+147)
		tmp = y - x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e+99], t$95$1, If[LessEqual[x, 5.2e+147], N[(y - x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3000000000000001e99 or 5.1999999999999997e147 < x

   1. Initial program 51.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

   5. Applied rewrites 25.5%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \color{blue}{\left(z - t\right)} \]

   8. Applied rewrites 5.3%

      \[\leadsto x + \left(y - \color{blue}{x}\right) \]

   9. Taylor expanded in x around inf

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} \]

   11. Applied rewrites 24.6%

       \[\leadsto x + \color{blue}{\left(a - t\right)} \]

   if -4.3000000000000001e99 < x < 5.1999999999999997e147

   1. Initial program 69.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

   5. Applied rewrites 12.4%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto x + y \cdot \color{blue}{\left(z - t\right)} \]

   8. Applied rewrites 26.2%

      \[\leadsto x + \left(y - \color{blue}{x}\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]

   11. Applied rewrites 26.1%

       \[\leadsto \color{blue}{y - x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 19.0% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ y - x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- y x))

C

double code(double x, double y, double z, double t, double a) {
	return y - x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = y - x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return y - x;
}

Python

def code(x, y, z, t, a):
	return y - x

Julia

function code(x, y, z, t, a)
	return Float64(y - x)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = y - x;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(y - x), $MachinePrecision]

Derivation

1. Initial program 65.0%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

5. Applied rewrites 15.7%

   \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z - t\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto x + y \cdot \color{blue}{\left(z - t\right)} \]

8. Applied rewrites 20.8%

   \[\leadsto x + \left(y - \color{blue}{x}\right) \]

9. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]

11. Applied rewrites 20.6%

    \[\leadsto \color{blue}{y - x} \]
12. Add Preprocessing

Developer Target 1: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -646122513817703/4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 1887201585041587/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))